We will use the Quadratic Formula to solve the given quadratic equation.
ax^2+ bx+ c=0 ⇔ x=- b± sqrt(b^2-4 a c)/2 a
We first need to identify the values of a, b, and c.
x^2-18x+65=0 ⇔ 1x^2+( -18)x+ 65=0
We see that a= 1, b= -18, and c= 65. Let's substitute these values into the Quadratic Formula.
The solutions for this equation are x= 18± 82. Let's separate them into the positive and negative cases.
x=18± 8/2
x_1=18+8/2
x_2=18-8/2
x_1=26/2
x_2=10/2
x_1=13
x_2=5
Using the Quadratic Formula, we found that the solutions of the given equation are x_1=13 and x_2=5. Finally, we will check our solutions by substituting their values into the original equation. Let's start with x=13
We will use the Quadratic Formula to solve the given quadratic equation.
ax^2+ bx+ c=0 ⇔ x=- b± sqrt(b^2-4 a c)/2 a
We first need to identify the values of a, b, and c.
x^2-2x+1=0 ⇔ 1x^2+( -2)x+ 1=0
We see that a= 1, b= -2, and c= 1. Let's substitute these values into the Quadratic Formula.
Using the Quadratic Formula, we found that the solution of the given equation is x_1=1. Finally, we will check our solution by substituting its value into the original equation.
